If a, b, c are distinct positive numbers, each different from 1, such that `[log_balog_ca-log_aa]+[log_ablog_cb-log_bb]+[log_aclog_ab-log_cc]=0` then `abc=`

If a,b,c be three distinct positive numbers, each different from 1 such that ("log"_ba"log"_ca-"log"_aa)+("log"_ab"log"_cb-"log"_b b)+("log"_ac"log"_bc-"log"_c c)=0 , then prove that abc=1

If a, b, c are distinct positive real numbers each different from unity such that (log_b a.log_c a -log_a a) + (log_a b.log_c b-logb_ b) + (log_a c.log_b c - log_c c) = 0, then prove that abc = 1.

If a, b, c are distinct positive numbers each being different from 1 such that (log_(b)a.log_(c)a-log_(a)a)+(log_(a)b.log_(c)b-log_(b)b) +(log_(a)c.log_(b)c-log_(c)c)=0 , then abc is a)0 b)e c)1 d)2

If a,b,c are distinct real number different from 1 such that (log_(b)a. log_(c)a-log_(a)a) + (log_(a)b.log_(c)b-log_(b)b) +(log_(a)c.log_(b)c-log_(c)C)=0 , then abc is equal to

If a,b,c are distinct positive real numbers each different from unity such that (log_(a)a.log_(c)a-log_(a)a)+(log_(a)b*log_(c)b-log b_(b))+(log_(a)c.log_(a)c-log_(c)c)=0 then prove that abc=1

If a,b,c are distinct real number different from 1 such that (log_(b)a. log_(c)a-log_(a)a) + (log_(a)b.log_(c)b.log_(c)b-log_(b)b) +(log_(a)c.log_(b)c-log_(c)C)=0 , then abc is equal to

If a,b,c be three such positive numbers (none of them is 1) that (log_(b)a log_(c )a-log_(a)a) + (log_(a)b log_(c )b-log_(b)b) + (log_(a)c log_(b)c-log_(c )c) = 0 , the prove that abc = 1.

If x is a positive real number different from 1 such that log_a x, log_b x, log_c x are in A.P then

If x is a positive real number different from 1 such that log_a x, log_b x, log_c x are in A.P then